I also thought that 7 possible solutions seemed an unlikely number, I thought it would have to be an even number.

So I solved it again and I found 7 solutions, even though I was sure it would not be 7.

I did not want to give too much away for other users who might not have solved the puzzle yet.

Hi Michaele

I see that you arrived at the same conclusion as me.

I take your point about not giving away too much so as not to spoil it for other users. I guess my earlier posts were a bit more specific than they needed to be, but I figured that anyone who had got that far had essentially solved the puzzle to all intents and purposes.

Apologies if I went too far.

Paul

Thank you, michaele, for your cooperation. I have seen in detail the Paul's spreadsheet and it's correct, it contains an additional solution that I had initially missed (due to swapping of numbers 5 and 6 in e7-e8 and h7-h8 ... ).

So the number of solutions must be 7 (I have played with the options but I do no find any other). You both paulv66 and michaele are right (great analysts ). However, as you both, I am very surprised and still wondering why (this will require me some time in the future, ... ). The michaele's considerations on cell h7 (which is the only cell with four possibilities, [5,6,7,8], are very interesting) (we could also start by f7 where the 5 is possible only once while 7 and 8 have both three possibilities, ... ), but my confusion is mainly related to the global concept of permutations in these situations.

Best, clm.

ddarthez

Posted on:Sun Feb 17, 2019 7:43 pm

Posts: 34Joined: Fri Jan 13, 2017 2:51 pm

Re: Congratulations on the site's 10 year anniversary!

Just a question for the time pressed users among us (like me at the moment): is there any time limit to submit solutions for the 10 year anniversary?

very surprised and still wondering why (this will require me some time in the future, ... ). The michaele's considerations on cell h7 (which is the only cell with four possibilities, [5,6,7,8], are very interesting) (we could also start by f7 where the 5 is possible only once while 7 and 8 have both three possibilities, ... ), but my confusion is mainly related to the global concept of permutations in these situations.

I think the quickest way to find the number of solutions is to start with the cell with the most pencil marks, if you start by looking at f7 (5 or 6) it does not help very much trying either 5 or 6 leaves several cells unsolved.My previous post was a bit vague, so below is a step by step method for finding all solutions.

The steps to determine the number of possible solutions are:1. Find the cell with the most values, cell h7 has 4 values (5,6,7,8) this indicates that there are at least 4 possible solutions.2. Try each value: h7=5 gives a solution h7=6 gives a solution h7=7 does not provide a single solution h7=8 does not provide a single solution3. There is no solution for 7 & 8, so do the same as steps 1&2 to find the number of possible solutions: h7=7 cells h4 and d7 have 3 values (this indicates a minimum of 3 solutions if h7=7), choose one of these cells (it does not matter which cell you use), and try each value, this will give 3 solutions h7=8 several cells have 2 values (this indicates a minmum of 2 solutions if h7=8), choose one of them and try each value, this will give 2 solutions.

This give a total of 7 solutions.

This is a little different to what I posted before, previously I had made testing h7=7 more complicated than it needed to be.This is quite quick to do, it seems like a lot, but there are only 14 cells with pencil marks so each possible value is quick and easy to test.

very surprised and still wondering why (this will require me some time in the future, ... ). The michaele's considerations on cell h7 (which is the only cell with four possibilities, [5,6,7,8], are very interesting) (we could also start by f7 where the 5 is possible only once while 7 and 8 have both three possibilities, ... ), but my confusion is mainly related to the global concept of permutations in these situations.

I think the quickest way to find the number of solutions is to start with the cell with the most pencil marks, if you start by looking at f7 (5 or 6) it does not help very much trying either 5 or 6 leaves several cells unsolved.My previous post was a bit vague, so below is a step by step method for finding all solutions.

The steps to determine the number of possible solutions are:1. Find the cell with the most values, cell h7 has 4 values (5,6,7,8) this indicates that there are at least 4 possible solutions.2. Try each value: h7=5 gives a solution h7=6 gives a solution h7=7 does not provide a single solution h7=8 does not provide a single solution3. There is no solution for 7 & 8, so do the same as steps 1&2 to find the number of possible solutions: h7=7 cells h4 and d7 have 3 values (this indicates a minimum of 3 solutions if h7=7), choose one of these cells (it does not matter which cell you use), and try each value, this will give 3 solutions h7=8 several cells have 2 values (this indicates a minmum of 2 solutions if h7=8), choose one of them and try each value, this will give 2 solutions.

This give a total of 7 solutions.

This is a little different to what I posted before, previously I had made testing h7=7 more complicated than it needed to be.This is quite quick to do, it seems like a lot, but there are only 14 cells with pencil marks so each possible value is quick and easy to test.

Thank you, michaele, your steps look very well. BTW, I assume that when you say " ... if you start by looking at f7 (5 or 6) it does not help ... " you are meaning e7 (since f7 has 3 possibilities: 5,7,8).Best, clm.